Based on theoretical calculations of a one-dimensional (1-D) photonic crystal, design criteria for omnidirectional (angle independent) structural colors have been developed as taught in co-pending U.S. patent application Ser. No. 11/837,529 (U.S. Patent Application Publication No. 2009/0046368, hereafter '529). As taught in '529, FIG. 1a illustrates a graph of a range to mid-range ratio equal to 0.2% for transverse magnetic mode (TM) and transverse electric mode (TE) of electromagnetic radiation plotted as a function of high refractive index versus low refractive index. This figure also shows two data points: one corresponding to an “ideal” multilayer stack made from a first material with a refractive index of 2.8 and a second material with a refractive index of 2.5; and another one corresponding to an actual fabricated multilayer stack made from vacuum deposition of TiO2 with a resulting refractive index of 2.3 and HfO2 with a resulting refractive index of 2.0.
Turning to FIG. 1b, a plot of reflectance as a function of incident angle illustrates the omnidirectional properties exhibited by the ideal multilayer stack when viewed from angles between 0 and 90 degrees. In contrast, FIG. 1c illustrates a reduction in the omnidirectional properties exhibited by the actual fabricated multilayer stack, in particular a decrease in the angle-independent reflectance from 0-90 degrees to 0-60 degrees.
On a plot of reflectance versus wavelength, an angle independent band of reflected electromagnetic radiation is the common reflectance of a multilayer stack when view from angles between 0 and theta (θ) degrees as illustrated by the range of wavelengths indicated by the double headed arrow in FIG. 1d. For the purposes of the present invention, this band of angle independent reflected radiation is measured at the average of the full width at half maximum (FWHM) for the two reflectance curves (0° and θ°) and can hereafter be referred to as an omnidirectional band when viewed between angles of 0 and θ degrees. It is appreciated that the extent of omnidirectional reflection, that is θ, for FIGS. 1b and 1c is 90 and 60 degrees, respectively.
It is appreciated that fabricating omnidirectional structural colors with less than desired indices of refraction can result in less than desired angle independence reflection. In addition, fabricating omnidirectional structural colors with materials that exhibit relatively high indices of refraction can be cost prohibitive. Therefore, a multilayer stack that provides omnidirectional structural color and can be made from materials that have relatively low indices of refraction would be desirable.